He starts to descend a grimy staircase. "As I descend deeper and deeper into the prison the conditions would become hotter and hotter and denser and denser until ... "

He gestures down a dark hole into the dusty depths of the building. "Down there, in the heart of the star, is the core. And it's in there that all the ingredients of life are made."

Some computer-generated models follow; a dying star roars and groans as the guitar plays on. Cox spray-paints chemical symbols onto the prison walls. He explains a bit about gravity and nuclear fusion. And then the money shot: the prison block literally implodes, crumbling into dust in the same amount of time a star takes to finally collapse.

This moment from Wonders of the Universe is classic BBC science documentary stuff: beautifully shot, dripping in money, and highly educational. Cox loves it. "It was very televisual; it was a stunt in a way, but actually it does illustrate the point very well."

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Cox is often referred to as the "rock star" scientist. It's not just cliche: he played keyboards for D:Ream (Things Can Only Get Better) in the 1990s while studying for his PhD in high-energy particle physics. Then, for a few years, he quietly beavered away at science.

But around 2005, the BBC's science team discovered he made for a charismatic talking head. That year he popped up in a documentary about Einstein, sitting in front of some "E=mc2" graffiti, looking like Keanu Reeves and sounding like an Oasis band member (Cox is from Oldham, near Manchester).

After a few years he graduated to the presenter role in a documentary on the Large Hadron Collider in Switzerland – his workplace. His hair was less shaggy, but his easy charm and boyish enthusiasm were undimmed, and he helped Britons get their heads around the world's biggest physics experiment and theories about the birth of the universe. A star was born (sorry).

Cox now has three Wonder series under his belt: lavish documentaries in which he travels to exotic locations around the world, using them as metaphors to understand the nature of the universe.

He pops up on chat shows and panel shows, explains science to current affairs programs and even joined Doctor Who actor Jenna-Louise Coleman on stage at the BAFTA television awards in May to present a prize. In August, he will tour Australia with his stage show, An Evening of Scientific Phenomena, complete with live experiments.

His programs have been credited with a surge in the number of British students who want to study physics – especially in Manchester – a phenomenon the media dubbed "the Cox effect", though he prefers to broadly credit the BBC's "year of science" in 2010, of which his Wonders of the Solar System was just one highlight.

The moment you stop investing in basic research ... your country will go into reverse.

In person, Cox is like his television persona, dialled down a little. We meet in a little cafe in Clapham – he is wearing sneakers and a grey tracksuit top – for the interview, which is a break in his day of writing for a book and his next documentary series.

Less than an hour later, I have a much better understanding of Einstein's theory of relativity, I've had a brief education in the basics of cosmology and why anomalies in the universe suggest the influence of extra dimensions, and I've learnt a bit about the Higgs field and its troubling role in dark energy.

"The amount of energy tied up in the Higgs field per cubic metre, it's more energy than the sun outputs in a thousand years," he tells me. "That should blow the universe to bits. It doesn't. Nobody knows why."

I'm not clear on what the Higgs field is, but I want to be. This is why Cox is such good television talent. He's not didactic or condescending, and not old-schoolmaster-BBC. He's genuinely excited by physics, and assumes either you already are, or you will be once you hear a bit more about it.

Cox isn't in science education TV for the fame or the money. He thinks it is his duty, that it makes the world a better place. "I've always thought science should be part of popular culture," he says. "It's way too important not to be. When I first started out, years ago [in TV], that was one of the motivating factors. Science is so important it has to be visible and in the conversation. So I've always thought scientists should be celebrities."

He passionately believes that putting science into the public arena improves society as a whole. It's not just about economic growth – though it has been demonstrated that economic growth follows investment in education and, in particular, science and engineering.

"A curiosity-led exploration of nature has always turned out historically to be useful," he says. "Without that basic premise that we should explore the universe and understand it, you wouldn't havescience."

One of his favourite quotes is from the birth of modern science in London, at the founding of the Royal Institute in the last years of the 18thcentury. Part of the founders' purpose was to convince the rich and powerful that engineering and science were the basis of civilisation. Chemist Sir Humphrey Davy and scientist Michael Faraday were under political pressure to justify the institute's existence. "Nothing is more fatal to the progress of the human mind than to presume ... that our triumphs are complete, that there are no mysteries in nature," Sir Humphrey responded.

Cox says every generation of scientists has had to fight complacency among society's rulers, the assumption among them being that most of what's useful has already been discovered.

"You can feel it now," he says. "When you've got difficult economic times, you see governments saying, 'Well, maybe we should cut back on this kind of blue-sky stuff.' It's just drivel. Imagine if that had happened in 1799 when the Royal Institute was being set up. Then, in the worst-case scenario, you don't get electricity."

He sees the direct ancestor of his documentaries in the institute's public lectures, which drove interest in science and persuaded politicians to pay attention. He sees the successors to Sir Humphrey and Faraday at the University of Manchester, where scientists discovered graphene, a substance with strength and conductivity that could revolutionise electronics and the aerospace industry.

"It could be that in 100 years' time you could not imagine a world without graphene," Cox says. And he is delighted that they isolated the new substance by applying household sticky tape to the tip of a pencil.

"We've got to be able to play with nature," he says. "The moment you stop investing in basic research, in your universities and knowledge, your country will go into reverse."

Cox still finds time for science. "I always wanted to be a scientist and that's what I think of myself as, even though most people think of me as some sort of light entertainer these days. He lectures at the University of Manchester, teaching quantum mechanics and relativity to first-year students.

He also continues to research. He is part of a team that runs experiments at the Large Hadron Collider, though it is undergoing maintenance, so he is working on a few theories on the troubling nature of cause-and-effect in the quantum basement of reality.

He has always been driven by a burning curiosity about the nature of the universe. In 1975, as a child, he wrote to NASA's jet propulsion laboratory, asking for pictures from the surface of Mars taken by the Viking spacecraft (NASA responded with some photographs).

Carl Sagan's seminal 1980s documentary Cosmos was a huge influence. "He put the science in a wider context," Cox says. "It was mainly an astronomy series, but he was polemical, he was absolutely clear: this is the way to figure it out. He said, and he was talking to the human race really, 'If you think like this then the world will be a better place.' It's a very lyrical, almost romantic approach, but it had that underlying element of polemic almost as the foundation of it, and I think that's important."

Cox says it's not always easy to resolve the "central tension" in scientific documentaries between information and entertainment. Sometimes he gets it right – when the building in Rio blew up, for instance. But sometimes it goes wrong. In his most recent series Wonders of Life, he used a great white shark to discuss the Reynolds number, which measures the balance between viscosity and "drag" in water and explains why submarines are a similar shape to sharks.

"But you know, there's a temptation in television to go, 'Wow, it's a shark!"' he says. "It got moved up to the front of the film, and I fought that. I don't usually lose battles but I lost that one, and I think it's worse for it. That piece of film looks like just any other channel, rather than a BBC documentary."

His next fight is over the title of his next series. He has dubbed it Human Universe, though he suspects marketers will want to stick a Wonders in there somewhere, a word he's now a bit sick of.

"It's the bit from the monkey to the space station. We've done the bit up to the monkey. So now it's like [the movie] 2001, the bit when the monkey waves the tool up in the air and it turns into a space station. It's that bit."

The first episode will be about humanity's "ascent into insignificance" – in 400 years, we've moved from the centre of the universe to an insignificant speck in one galaxy among 350 billion.

"But it is an ascent," Cox says, with his customary infectious enthusiasm, "because we've understood that."

Brian Cox: An Evening of Scientific Phenomena is at the Capitol Theatre on August 15 and 16.